# Summands in locally almost square and locally octahedral spaces

## TL;DR

This paper investigates whether certain geometric properties of Banach spaces, such as local almost squareness and octahedrality, are inherited by component spaces from their absolute sum constructions.

## Contribution

It provides new insights into the inheritance of geometric properties in Banach space sums, specifically analyzing conditions under which properties pass from sum spaces to summands.

## Key findings

- Conditions identified for properties to pass from sum to summands
- Counterexamples showing limitations of inheritance
- Characterizations of spaces with these properties

## Abstract

We study the question whether properties like local/weak almost squareness and local octahedrality pass down from an absolute sum $X\oplus_F Y$ to the summands $X$ and $Y$.